5 Interval inversion

Interval inversion refers to turning the interval upside down. The top note becomes the bottom note, and the bottom note becomes the top note. Inversion is accomplished by moving the bottom note up one octave or moving the top note down one octave.

Notice that the number size of an interval plus the number size of its inversion always adds up to 9:

A 2nd inverts to a 7th.
A 3rd inverts to a 6th.
A 4th inverts to a 5th.
A 5th inverts to a 4th.
A 6th inverts to a 3rd.
A 7th inverts to a 2nd.

When an interval is inverted, its quality usually changes as well as its number size. The only exception are perfect intervals.

An augmented interval when inverted becomes diminished.
A major interval when inverted becomes minor.
A perfect interval when inverted remains perfect.
A minor interval when inverted becomes major.
A diminished interval when inverted becomes augmented.

(Just a note about notation.  Accidentals should always be on the same line or space as the note it is affecting. Notice the example above of the A2.  The sharp is on the same line as the F, and the flat is on the same space as the E. This correct notation is the only way a reader would be able to tell which accidental goes with which note. Make sure you observe this rule both when reading music as well as when writing music.)

 Interval inversion

 Check yourself:
 

Using interval inversions can be helpful in determining larger intervals if the number of half steps for the smaller intervals is memorized:

m2 = 1 half step
M2 = 2 half steps (or 1 whole step)
m3 = 3 half steps (or 1 1/2 steps)
M3 = 4 half steps (or 2 whole steps)

For example, what is a M7 above G?

Instead of thinking about a M7 above G, think of its inversion below G.
The inversion of a M7 is a m2 (half step).
A m2 (half step) below G is F#; therefore, a M7 above G is also F#.

Try this one on your own:

What is a m6 above F-sharp?

A M3 below F-sharp is D; therefore, a m6 above F-sharp is also D.
MTSB Lesson 6, practice interval inversion